Abstract: Graphene nanoribbons GNRs with widths down to 16 nm have been characterizedfor their current-carrying capacity. It is found that GNRs exhibit animpressive breakdown current density, on the order of 10^8 A-cm2. The breakdowncurrent density is found to have a reciprocal relationship to GNR resistivityand the data fit points to Joule heating as the likely mechanism of breakdown.The superior current-carrying capacity of GNRs will be valuable for theirapplication in on-chip electrical interconnects. The thermal conductivity ofsub-20 nm graphene ribbons is found to be more than 1000 W-m-K.